The Value Of The Elastic Rod Model Equations Spectral Method

Elastic rod, an important physical model for scientific problems as well as engineering projects, attracted great attention in biological research in recent years. One of the most important approaches in studying elastic rods is numerical method. To improve the precision of numerical simulation, high precision methods on dynamic models of an elastic rod are studied in this paper. The main results includei) A numerical method for solving structural model of an elastic rod is given. By using Fourier spectral basis in Galerkin method to solve nonlinear Schr(?)dinger equation based on Kirchhoff hypothesis, numerical solution of spectral precision can be obtained with relatively less computation.ii) The dynamical equations of an elastic rod is a nonlinear partial differential/algebraic equation system. Spectral methods for solving the equations of this kind usually use spectral methods to discrete spatial variables but Runge-Kutta method to discrete temporal variable, therefore the precision usually can not reach spectral precision. A new method which combines the spectral method on spatial variables and spectral deferred correction method on temporal variables is given in this paper. The method is of spectral precision, A-stable and symplectic, which means more reliable for long time numerical Simulation. Spectral methods based on Fourier basis as well as that based on Lagendre Orthogonal polynomials basis, are discussed in this paper for different initial value and boundary value conditions and different need of numerical simulation. In addition, pre-conditioning acceleration skill is used to overcome the computational complex.